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THEORETICAL ASSUMPTIONS FOR AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY
STED Journal, 2023 Understanding elliptic curves contributed to solving mathematical problems in number theory that had been unsolved for centuries. Elliptic curves were also used in solving one of the millennial problems, which is Fermat's last theorem.
Ognjen Milivojević, Boris Damjanović
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Lam\'e polynomials, hyperelliptic reductions and Lam\'e band structure
, 2004 The band structure of the Lam\'e equation, viewed as a one-dimensional Schr\"odinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion relation, and a ...
Arscott F.M +11 more
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An exploration of affine group laws for elliptic curves
Journal of Mathematical Cryptology, 2011 Several forms of elliptic curves are suggested for an efficient implementation of Elliptic Curve Cryptography. However, a complete description of the group law has not appeared in the literature for most popular forms.
Hisil Huseyin +3 more
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A NEW PROPOSED METHOD FOR SOLVING AN ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM
Journal of Kufa for Mathematics and Computer, 2012 In this work, we present a new approach for solving Elliptic Curve Discrete Logarithm Problem. This method provides a new access to the field of attacking methods the Elliptic Curve Cryptosystems.
Ammar Ali Neamah
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Journal of Number Theory, 1993 Let \(J_ 0(N)/ \mathbb{Q}\) denote the Jacobian of the modular curve \(X_ 0(N)/ \mathbb{Q}\). Fix a prime \(p \geq 5\), and let \(K\) denote the maximal unramified extension of \(\mathbb{Q}_ p\). Given an abelian variety \(A/K\), the connected component of zero of the special fiber of its Néron model is an extension of an abelian variety of dimension \(
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Ray class fields generated by torsion points of certain elliptic curves [PDF]
, 2010 We first normalize the derivative Weierstrass $\wp'$-function appearing in Weierstrass equations which give rise to analytic parametrizations of elliptic curves by the Dedekind $\eta$-function.
Dong +3 more
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A note on Galois embeddings of abelian varieties
, 2017 In this note we show that if an abelian variety possesses a Galois embedding into some projective space, then it must be isogenous to the self product of an elliptic curve.
Auffarth, Robert
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Classification of Elements in Elliptic Curve Over the Ring 𝔽q[ɛ]
Discussiones Mathematicae - General Algebra and Applications, 2021 Let 𝔽q[ɛ] := 𝔽q [X]/(X4 − X3) be a finite quotient ring where ɛ4 = ɛ3, with 𝔽q is a finite field of order q such that q is a power of a prime number p greater than or equal to 5.
Selikh Bilel +2 more
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Mathematics, 2022 The remote authentication scheme is a cryptographic protocol incorporated by user–server applications to prevent unauthorized access and security attacks.
Fairuz Shohaimay, Eddie Shahril Ismail
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Elliptic curves with maximal Galois action on their torsion points
, 2008 Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, \rho_E : Gal(\bar{k}/k) \to GL_2(\hat{Z}).
Zywina, David
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